ii-7 simms multibody modelling for impact biomechanics delhi 2013
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II-7 Simms Multibody Modelling for Impact Biomechanics Delhi 2013TRANSCRIPT
Introduction to Multibody Modelling for
Impact Biomechanics Applications
Dr Ciaran Simms FTCD
Delhi
December 2013
Ciaran Simms Multibody Methods
Mechanical dummies
Mathematical
modelling
Virtual crash
environment
CANNOT GENERALLY CRASH TEST HUMANS…NEED MODELLING METHODS
Volunteers
Animals
Cadavers
2
pSgtztx
2
2
11
Ciaran Simms Multibody Methods
Model Complexity
3
Need to decide your research question to determine
appropriate model complexity
Make everything as simple as possible, but no
simpler (Einstein)
More complex models have more outputs, but also
more inputs – often increased uncertainity
Ciaran Simms Multibody Methods
Particle models can predict pedestrian trajectories
MIXED SINGLE SEGMENT MOMENTUM AND PARTICLE MODELS TO
ESTIMATE IMPACT SPEED FROM PROJECTION DISTANCE
But what about effects of vehicle shape?
Simms & Wood, Springer 2009
Ciaran Simms Multibody Methods
Models based on conservation of Momentum
Accounts for geometry and inertia and captures principal
kinematics even with a single segment model WITHOUT
knowledge of vehicle stiffness.
Ciaran Simms Multibody Methods
Momentum based models
Can assume plastic contacts and rigid body relations and then
do not need specific contact stiffnesses to proceed – good for
general analysis, also essence of PC Crash
Assume step changes in velocity components when contacts
occur: hence no injury predictions
HOWEVER, for force time history modelling need an ordinary
differential equation approach
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Ciaran Simms Multibody Methods
Simms & Wood, Springer 2009
ORDINARY DIFFERENTIAL EQUATION FORMULATION
xX
z
B – vehicle contact on leg
C – vehicle contact on head
D – feet contact with ground
FC
Ciaran Simms Multibody Methods
How to get velocities & displacements from this kind of model ?
eg spring mass system, stiffness
Initial conditions:
Newton II:
Euler integration
Similar approach to get displacements (normally
coupled solutions to two 1st order ODEs used)
Time marching solution using initial conditions
ii txktx
knownxx
0,0
txtx ,
iiiii tttxtxtx
11
k
k
Ciaran Simms Multibody Methods
Multibody Modelling
To capture body articulation, need to be able to
combine a number of links with kinematic joints and
add joint stiffnesses
Need to be able to handle hysteresis and damping
and non-linearity in contacts
Can then get force time and acceleration time
behaviour of all components
Assumption that all links remain rigid 9
Ciaran Simms Multibody Methods
ONE/TWO SEGMENT ORDINARY DIFFERENTIAL EQUATION FORMULATION
Simms & Wood, Springer 2009
Ciaran Simms Multibody Methods
MULTIBODY MODELS: eg MADYMO – commercial code to make using these models easier
CAN PREDICT FORCES, ACCELERATIONS, but essentially
what you put in is what you get out!
Model itself is not so interesting, it is what it can tell you...
Simms & Wood, Springer 2009
Madymo Pedestrian impact simulations
Ciaran Simms Multibody Methods
12
Rigid
Body
Dynamics
• Tree structure
• Rigid bodies
• Surfaces
• Contacts
• Integration
Adapted from TNO Madymo
So how does it work?
Ciaran Simms Multibody Methods
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Multibody systems mathematically simulate the motion of multiple
rigid bodies connected by joints to form multiple systems
Force models and contact interactions are applied to the rigid bodies
and the motions caused by these forces are calculated with
numerical integration methods
working with FORCES and DISPLACEMENTS, NOT with STRESS
and STRAIN (as used in FE models)
lumped parameter models (like a free body diagram)
Multibody approach
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Tree Structure
unique sequence of bodies and kinematic joints
2 systems 3 systems, resp., 7 bodies1 body and 5 bodies
1 system with 12 bodies
A System is one or more chains of one or more rigid bodies Adapted from TNO Madymo
Ciaran Simms Multibody Methods
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Rigid Body
A rigid body has constant mass & rotational inertia but no geometrical properties of its own
Connected to other bodies within a multibody system by joints
Can be connected to other bodies with springs and dampers
Planes, ellipsoids, etc can be connected to a rigid body
Define mass, inertia and centre of gravity wrt local coordinate system
Positions and orientations of rigid bodies are computed
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Rigid Body Relations
Two points on a rigid body have a relative velocity
defined by the distance between them and the
angular velocity of the body
Can be expressed in vector format as:
16 ABBAAB
ABBAAB
ABAB
rvv
rv
vvv
/
//
/
B
A
Bv
Av
Ar
BA
Ciaran Simms Multibody Methods
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Multibody Surfaces
Surfaces for contact evaluations and visualising
– PLANES
– ELLIPSOIDS
– CYLINDERS
FE Mesh may also describe an arbitrary surface, but
this is a ‘null’ material and no strain-stress calculation
is performed
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
(Hyper-) Ellipsoids
A (hyper-)ellipsoid is defined by
The location of the centre
The degree n
The semi-axes a, b and c
The orientation of the semi-axis
xe
a
n
ye
b
n
ze
c
n
1
ye
2D ellipsoid 3D ellipsoid
ze
xe
x y
z
ze
ye
z
y
cb b
c
a
n = 2
n = 8
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
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Integration Method and Time Step
Numerical integration of the system’s
differential equation’s of motion
Usually Runge Kutta or Euler integration
Euler:
Forward integration is conditionally stable:
need to check timestep small enough
iiiii tttxtxtx
11
Ciaran Simms Multibody Methods
Timestep importance
Spring mass system: period T = 0.2 ps
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
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Contact between multibody surfaces.
An action and reaction force is applied on the corresponding
bodies depending on the surface penetration
Contact force consists of
Elastic force Fe(l)
Damping force Fd
Friction force Ff
Freaction
Faction
Ff
Fe
Fd
λ
Multibody contacts
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Relative Velocity in a Contact
Velocity used for calculation of damping and friction force is
the relative velocity of the contacting bodies at the point of
application of the contact force
P
Vnorm
V
Vplane
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Elastic Force
user defined force-penetration loading (L)
and unloading (U) function
Can measure experimentally and use as
input
Hysteresis can be specified, often very
important for realistic kinematics
Dynamic amplification factor can account
for dependency of the elastic force on the
rate of the penetration
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Elastic force is found from observed penetration between surfaces in contact at a given timestep
p1
l
p2
ellipsoid
plane
p1
p2
ellipsoid
plane
ellipsoid 2
l1l2
l
Adapted from TNO Madymo
Ciaran Simms Multibody Methods
Newton-Euler Equations of Motion
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𝑭 = 𝑮
(linear)
𝑴 = 𝑯 = 𝐼 𝝎 + 𝝎 ×𝑯
(angular)
In MADYMO, these equations of Motion are solved for
systems of rigid bodies using the Principle of Virtual Power
Ciaran Simms Multibody Methods
A study of pedestrian head translation, rotation and impact velocity: The influence of vehicle speed,
pedestrian speed and pedestrian gait
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Case study 1: Ciaran Simms Multibody Methods
• Influence of vehicle speed, pedestrian speed and pedestrian gait on
pedestrian post impact kinematics have not been quantified - MADYMO
• Transverse translation influences injury severity due to variations in local
vehicle stiffness
• Head rotation is related to pedestrian stance at impact which influences the
overall kinematics
• Head impact velocity influences head injuries
Ciaran Simms Multibody Methods
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Baseline simulation Transverse Offset
Pedestrian Gait cycle Head rotation about
vertical axis
Ciaran Simms Multibody Methods
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Transverse offset varies cyclically with pedestrian gait
Modelling Results: Transverse Offset Ciaran Simms Multibody Methods
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Modelling Results: Transverse Offset
Transverse Offset depends also on vehicle speed
Ciaran Simms Multibody Methods
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Modelling Results: Transverse Offset
Transverse offset reduces
with vehicle speed Transverse offset increases
with pedestrian speed
Ciaran Simms Multibody Methods
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Modelling Results: Head Rotation
Head Rotation reduces with
vehicle speed
Head Rotation increases
with vehicle speed
Ciaran Simms Multibody Methods
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Modelling Results: Head Rotation
Positive and Negative Regions of Pedestrian Head Rotation
Ciaran Simms Multibody Methods
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Modelling Results: head impact velocity
Head impact speed is a linear function of vehicle speed
Largely independent of pedestrian speed
Ciaran Simms Multibody Methods
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Modelling Results: Analysis
Transverse Offset is a linear function of ratio of Pedestrian to Vehicle speed
Ciaran Simms Multibody Methods
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Modelling Results: Head rotation
Head Rotation is a linear function of ratio of Pedestrian to Vehicle speed
Ciaran Simms Multibody Methods
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• Transverse Offset, Head rotation and head impact
speed vary cyclically and significantly with gait
• First quantification of the influences of pedestrian
speed and stance on transverse offset and head
rotation, both of which may sometimes be available in
individual pedestrian accident cases.
Study conclusions Ciaran Simms Multibody Methods
The Influence of Vehicle Shape on Pedestrian Ground Contact
Mechanisms
Presented to IRCOBI conference Krakow 2011
CK Simms1, Tom Ormond1 & DP Wood2
1Centre for Bioengineering, Trinity College, Dublin, Ireland 2Denis Wood Associates, Dublin, Ireland
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Case study 2: Ciaran Simms Multibody Methods
• Injuries from the vehicle contact and ground contact phases.
• High variability of ground contact injuries.
• Vehicle Shape is important for ground related pedestrian injuries:
• Ground contact head injuries more frequent for high Bonnet Leading Edges
• Ground contact injuries from newer cars less significant
• Ground contact: Passenger cars (ground contact is 7% of head injuries)
Light Trucks and Vans (ground contact is 39% of head injuries)
Simms & Wood, Springer 2009
41
Ciaran Simms Multibody Methods
Research approach
What is the kinematic explanation why high-fronted vehicles
result in more severe head/ground injuries for pedestrians than
collisions with conventional cars?
Research question
Multibody models (Madymo) to include effects of vehicle
speed, vehicle shape & pedestrian size and gait stance.
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Ciaran Simms Multibody Methods
Madymo Simulation Setup
Cars and SUV models created in Madymo
Contact surfaces & characteristics for bumper,
BLE, bonnet top and windscreen.
The midsize male/small female
Walking pedestrian struck from the side, leading
leg or trailing leg struck first
Vehicle impact speed 25-35 km/h
72 simulations performed
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Ciaran Simms Multibody Methods
Results
Mechanism 1: 46% of cases: a wrap trajectory, rotation (90o< α< 180o)
with the head hitting the ground first, followed by the body.
Angle of impact with ground correlates with HIC score (r2= 0.56).
Six Mechanisms of ground contact accounted for 94% cases
Distinguished by amount & direction of rotation of the body at ground contact
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Ciaran Simms Multibody Methods
Results
Mechanism 2:14% of cases: Rotation (0o< α< 90o) insufficient to raise
body above the head before ground contact occurs
Body strikes the ground first followed by the head
Mechanism 3:12% of cases: Rotation (180o< α< 270o).
Head strikes ground first, then body
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Ciaran Simms Multibody Methods
Results Mechanism 4:15% of cases: Whole body rotation (α> 270o) occurs &
body contacts the ground first, then head
Mechanism 5: BLE sufficiently above the pedestrian centre of gravity
(α<90o). Pedestrian pushed forward, body contacts ground first.
Mechanism 6: shoulder contacts ground first - head protection
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Ciaran Simms Multibody Methods
HIC score by mechanism type
HIC score strongly depends on Mechanism
HIC for Mechanism 1 & 2 >> HIC for Mechanisms 3-6.
Mech 1
(90o<α<180o)
Mech 2
(0o<α<90o)
Mech 3
(180o<α< 270o)
Mech 4
(α>270o)
Mech 5
(α<90o)
Ciaran Simms Multibody Methods
Impact mechanism by vehicle type
Instances of Mechanism 1 increase with increasing vehicle size (bonnet
height) as far as midsized SUV (BLE height of about 1 m)
Mechanism 4 (α>270o) only occurs with cars, Mechanism 5 (α<90o) only
occurs with large SUV model.
Mech 1
(90o<α<180o)
Mech 2
(0o<α<90o)
Mech 4
(α>270o)
Mech 5
(α<90o)
Mech 3
(180o<α< 270o)
Ciaran Simms Multibody Methods
Results/Discussion
Comparative study: focus on trends, no validation data
Average HIC for different vehicles versus normalized bonnet height showed r2
values of .74 for midsized male.
HIC from ground independent of vehicle speed (r2= 0.04).
For Mechanism 1 (46% of cases), angle of body impact with the ground
correlated with HIC score (r2= 0.56) and angle of impact also decreased with
bonnet height (r2= 0.37).
Simple Explanation: High HIC occurs when impact angle is low
and rotation < 180° so that body rotation causes head to move
towards ground
Direct influence of body angle on HIC new
Lower bonnets cause more body rotation, so that by time of ground contact
body is rotating away from ground.
For large SUV, reduced rotation means very few Mechanism 1 cases, but
many Mechanism 2 cases
Ciaran Simms Multibody Methods
Conclusions
For speed range 25-35 km/h, variations in normalised bonnet height accounts
for up to 74% of variation in ground HIC.
Most common & worst scenario is wrap trajectory where head hits ground first
with body rotating head towards the ground – then ground HIC depends on
body angle and direction of body rotation.
The angle of impact with the ground is correlated with the HIC (r2= 0.56) and
bonnet leading edge height (r2= 0.37).
When the body is rotating away from the ground at ground contact, HIC is
reduced - more likely to occur for car impact than for SUV impact cases
Since impact angle decreases with bonnet height, these findings help to
explain why high-fronted vehicles result in more significant head injuries in
ground contact.
Ciaran Simms Multibody Methods
Conclusions for MB modelling
Multibody models are fast
and efficient for whole body
simulations
Can predict all structural
parameters like linear and
angular acceleration,
bending moments and force
These are easily related to
common injury criteria
Need to be aware of model
limitations and validation
extent
No means to evaluate tissue
stress and strain
Contacts are chief modelling
challenge
Despite popularity and
potential of FE modelling,
relative simplicity of MB
models will ensure their
continued usage in the
future for fundamental
insights – don’t give up on
this method
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Ciaran Simms Multibody Methods